Pith Number

pith:BHN5RSSL

pith:2015:BHN5RSSLOTDTRWJJ2SEJK4BHZO

not attested not anchored not stored refs pending

First order local invariants of planar caustics

Mar\'ia del Carmen Romero Fuster, Ra\'ul Oset Sinha

arxiv:1512.05943 v2 · 2015-12-18 · math.AT · math.DG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BHN5RSSLOTDTRWJJ2SEJK4BHZO}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T00:52:58.907916Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

09dbd8ca4b74c738d929d488957027cb988d427e2f733b7f51ce2d96316c34d5

Aliases

arxiv: 1512.05943 · arxiv_version: 1512.05943v2 · doi: 10.48550/arxiv.1512.05943 · pith_short_12: BHN5RSSLOTDT · pith_short_16: BHN5RSSLOTDTRWJJ · pith_short_8: BHN5RSSL

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/BHN5RSSLOTDTRWJJ2SEJK4BHZO \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 09dbd8ca4b74c738d929d488957027cb988d427e2f733b7f51ce2d96316c34d5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8d78f052c83cd5ae943e075d1090823822ea832de66ad20528ef12a3de5d4db7",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2015-12-18T13:27:57Z",
    "title_canon_sha256": "298f0511e9630a0b3b0569ff3349ca6ac5c16f6a9347a9ac1b314f3d24dd2841"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.05943",
    "kind": "arxiv",
    "version": 2
  }
}